They live to improvise, but they’re no jam band. They embrace mandolins and banjos, but they ain’t country, either.

Yonder Mountain String Band knows no specific genre. The underground Colorado four-piece formed in 1998 and embraced roots-rock before Zac Brown ever picked up a guitar. They’ve released five studio albums, played for President Obama, and continue to make music on their own label — and on their own terms. Just don’t call it “bluegrass.”

Bassist Ben Kaufmann broke it down for us as his band prepped for its Jannus Live show Saturday (tickets are $19.99; click here for details).

New bands seem to be in a hurry to find fame. What’s kept you going?

Most people don’t know who we are. If you ask 100 people on the street in Central Park or in Times Square if they’ve ever heard of us, 99 would say no. And yet we fill out Red Rocks (Amphitheatre in Morrison, Colo.) every year, and we played the frickin’ Democratic National Convention. … We’ve slowly generated this following over 12 years now and to me that feels correct, in a way. … It really comes down to the whole thing of, “Are you going to buy into this sort of false misinformation of what it means to be a rock star?”

YMSB predates the likes of the Avett Brothers and Zac Brown Band. Has their recent success given you more confidence that Americana and bluegrass music has a place in the mainstream?

Not right now in America, no. I think it’s still a very niche thing. I think that we saw the height of its mainstream-ness with O Brother, Where Art Thou?, and that was what, 10 years ago? I think that’s as much as it will reach the masses. You can find examples of popular music with banjos in it now, but apart from that it has nothing to do with bluegrass music.

I have to admit I’m not a fan of bluegrass today. I never listen to modern bluegrass. Ever. I’m just not interested in it. There’s nothing really that feels very relevant to me. It’s just people singing about a time and place in America that doesn’t exist anymore. And similarly I have to say I don’t consider what Yonder Mountain does to be bluegrass. Although it’s related to and born of that tradition, the band when we formed were already two or three generations removed from bluegrass music. … I think the nature of the beast and the nature of having the bluegrass or string-band association means that people can very easily dismiss you because they see the name, or have some association with what your music might be, and then conclude that they won’t like it without ever having heard it. So that’s our challenge.

How will you meet that challenge in 2011?

If we can crack London, I would feel tremendously proud. I’m looking forward to getting overseas to places where people don’t have any sort of preformed ideas. If you say “bluegrass” to an Australian person, that means something totally different than if you say “bluegrass” to someone in America. If you say “banjo” to someone in Japan, the connotations are completely different.

What about the word “yonder?”

That is an old word. It doesn’t show up a lot in our modern vocabulary. While it does have its roots in this sort of dated rural usage, to me it means my band is a deviation from what you’re going to find here; “It’s over there.” There are so many popular bands, even within the scenes that we find ourselves in, that are extraordinarily popular and have the worst names for their bands. If you gave me a year, I couldn’t think of a worse name for a band, and their popularity is massive. Stadium popular.

Which band is that?

Because I’m liable to run into them this summer, I can’t say it. (laughs) Google “stupid jam-band names,” and I’m sure you’ll come up with a hundred.